We study in this chapter the main properties of Lorentz spaces L p,q (X) with 0 < p ≤ +∞ and 0 < q ≤ +∞. We start with a study of Marcinkiewicz spaces L p,∞ using the distribution function d f and then we present general Lorentz spaces L p,q by using the decreasing rearrangement function f * and the maximal function f * *. Normability, Convolution, Duality of these functional spaces are the main core of this chapter.